A bit more research shows I need some sort of signal processing between the RX and the PWM signal for the motor driver circuit.

The signal from the RX is a PWM signal where the length of the high pulse is what's important (example: 150ms long pulse is neutral or half way on servos. 100ms pulse is the shortest (or all the way one way on a servo) and 200ms is longest (all the way the opposite way). There is then a low pulse for some time after it.

The signal the motor driver circuit needs is a PWM signal where the duty cycle of the pulses is important. If the pulse spends 50% of the time up and 50% down it will drive the motor at half speed. 75% up/25% down the motor is at 3/4 speed.

I'm thinking of buying an Arduino Uno for this task.